BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Tanja Isabelle Schindler (Scuola Normale Superiore di Pisa)
DTSTART:20201208T133000Z
DTEND:20201208T143000Z
DTSTAMP:20260423T021444Z
UID:OWNS/26
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/26/">Li
 mit theorems on counting large continued fraction digits</a>\nby Tanja Isa
 belle Schindler (Scuola Normale Superiore di Pisa) as part of One World Nu
 meration seminar\n\n\nAbstract\nWe establish a central limit theorem for c
 ounting large continued fraction digits $(a_n)$\, that is\, we count occur
 rences $\\{a_n>b_n\\}$\, where $(b_n)$ is a sequence of positive integers.
  Our result improves a similar result by Philipp\, which additionally assu
 mes that bn tends to infinity. Moreover\, we also show this kind of centra
 l limit theorem for counting the number of occurrences entries such that t
 he continued fraction entry lies between $d_n$ and $d_n(1+1/c_n)$ for give
 n sequences $(c_n)$ and $(d_n)$. For such intervals we also give a refinem
 ent of the famous Borel–Bernstein theorem regarding the event that the n
 th continued fraction digit lying infinitely often in this interval. As a 
 side result\, we explicitly determine the first $\\phi$-mixing coefficient
  for the Gauss system - a result we actually need to improve Philipp's the
 orem. This is joint work with Marc Kesseböhmer.\n
LOCATION:https://researchseminars.org/talk/OWNS/26/
END:VEVENT
END:VCALENDAR